The pKa of HCN is 9.30. The pH of a solution prepared by mixing 2.5 moles of KCN and 2.5 moles of HCN in water and making up the total volume of 500 mL is:

To determine the pH of a solution containing equal moles of HCN and KCN, we can use the Henderson-Hasselbalch equation for buffer solutions:

pH = pKa + log([A⁻]/[HA])

Here:

• pKa of HCN = 9.30
• [A⁻] (conjugate base, CN⁻) = concentration of KCN
• [HA] (weak acid, HCN) = concentration of HCN

Given:

• Moles of HCN = 2.5 moles
• Moles of KCN = 2.5 moles
• Total volume of solution = 500 mL = 0.5 L

First, calculate the concentrations:

• [HCN] = 2.5 moles / 0.5 L = 5 M
• [KCN] = 2.5 moles / 0.5 L = 5 M

Since the concentrations of HCN and KCN are equal, the ratio [A⁻]/[HA] = 1.

Applying the Henderson-Hasselbalch equation:

• pH = pKa + log(1)
• pH = 9.30 + log(1)
• pH = 9.30 + 0
• pH = 9.30

Therefore, the pH of the solution is 9.30.